PROOF + READER = DELUXE
What is this puzzle?
Solve the addition alphametic puzzle where PROOF + READER = DELUXE. Each letter represents a unique digit from 0-9. No number starts with zero.
Difficulty: hard · Category: addition · Unique letters: 10
This hard-level addition alphametic puzzle features 10 unique letters (A, D, E, F, L, O, P, R, U, X). In the equation PROOF + READER = DELUXE, each letter maps to a distinct digit from 0 to 9. The leading letters P and R and D cannot represent zero — this is your first constraint. To solve this efficiently, focus on letters that appear in multiple positions across the equation — these are the most constrained and often the easiest to determine first. This is a challenging puzzle that requires systematic use of carry analysis, parity checking, and elimination. Start by listing all constraints, then methodically eliminate impossible digit assignments.
- This addition alphametic has 10 unique letters to determine.
- Leading letters: P, R, D. None of these can be zero.
- All 10 digits (0–9) are used, one per letter.
- Start from the rightmost column (units place) and work left, tracking carries between columns.
- With two addends, each column can produce a carry of at most 1.
- With many unique letters, use elimination and constraint tracking to narrow down possibilities step by step.